The review, which should take a few months, will complement an ongoing exercise to stress test Spain's banking sector by consultors Oliver Wyman and Roland Berger, whose first results are expected around mid-June.
"I can confirm (the names)," the source said.
Spain's Prime Minister Mariano Rajoy on Saturday said his government would have a clear view of how much money will be needed to recapitalize troubled lenders by the end of June.
He also said the government would make clear by then how it intends to inject the money.
Economy Minister Luis De Guindos said earlier this week that Spain would likely go to the markets to find the 19 billion euros ($23.5 billion) nationalized lender Bankia
Senior EU officials have said privately that the country should instead seek a loan from the European bailout fund but that would necessarily come with tough conditions and a high political cost Rajoy is not willing to assume.
The European Stability Mechanism (ESM), due to enter into force on July 1st, has the capacity to lend money to banks but the request has to be made by the state, which receives the money and then transfers it to the lenders.
German Chancellor Angela Merkel has so far opposed calls from other European leaders, including from Rajoy or France's President Francois Hollande, to change the rules and allow direct recapitalizations of the banks.
(Reporting by Julien Toyer; Editing by Mike Nesbit)
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